Question

Solve the initial value problem below for the Cauchy-Euler equation

t^2y"(t)+10ty'(t)+20y(t)=0, y(1)=0, y'(1)=2

y(t)=

Answer #1

solve the Cauchy-Euler Initial value
9t2y''' + 15ty'+y= 0 with y(1) = 6 and y'(1) =1

For the initial value problem
• Solve the initial value problem.
y' = 1/2−t+2y withy(0)=1

Solve the initial value problem: y''−2y'+y=e^t/(1+t^2), y(0) =
1, y'(0) = 0.

Solve the differential equation with initial value
y''−2y'+y=e^t/(1+t^2), y(0) = 1, y'(0) = 0.

For 2y' = -tan(t)(y^2-1) find general solution (solve for y(t))
and solve initial value problem y(0) = -1/3

use the laplace transform to solve initial value
problem
y"+4y'+20y=delta(t-2)
y(0)=0, y'(0)=0
use step t-c for uc(t)

x^2y'' − 3xy'+ 4y = 0 ; y(1)=5 y'(1)=3
differential equation using the Cauchy-Euler method

x^2y'' − 3xy'+ 4y = 0 ; y(1)=5 y'(1)=3
differential equation using the Cauchy-Euler method

solve the initial value problem y''-2y'+5y=u(t-2) y(0)=0
y'(0)=0

Solve the following initial value problem.
y′′ − 9y′ + 20y = 3x +
e5x, y(0)
= 0, y′(0) = 2

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